Check the solution to "Factor each polynomial. 12t4−t2−35"

Gregory Emery

Answered question

2021-12-14

Factor each polynomial.

12 t^{4} - t^{2} - 35

Ethan Sanders

Beginner2021-12-15Added 35 answers

Step 1
To Factor polynomial.

P (x) = 12 t^{4} - t^{2} - 35

Take

u = t^{2}

P (x) = 12 u^{2} - u - 35

Now by using quadratic formula,

u = \frac{- b \sqrt{b^{2} - 4 a c}}{2 a}

Step 2

P (x) = 12 u^{2} - u - 35

u = \frac{- 1 \pm \sqrt{{(- 1)}^{2} - 4 (12) (- 35)}}{2 (- 1)}

u = \frac{- 1 \pm \sqrt{1 + 1680}}{- 2}

u = \frac{- 1 \pm \sqrt{1681}}{- 2}

u = \frac{- 1 \pm 41}{- 2}

u = \frac{- 1 + 41}{- 2}

and

u = \frac{- 1 - 41}{- 2}

u=-20 and u=21
Plug in

u = t^{2}

t^{2} = - 20

and

t^{2} = 21

t^{2} = - 20

is not possible
Therefore,

t^{2} = 21

t = \pm \sqrt{21}

Melinda McCombs

Beginner2021-12-16Added 38 answers

Step 1
Given polynomial is,

12 t^{4} - t^{2} - 35

.
It is factorize as follows:

12 t^{4} - t^{2} - 35

.
Let

u = t^{2}

12 t^{4} - t^{2} - 35 = 12 u^{2} - u - 35

Step 2
Further simplification,

12 u^{2} - u - 35 = (3 u + 5) (4 u - 7)

= (3 t^{2} + 5) (4 t^{2} - 7)

This is the required answer.

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